**Time**: 3:45pm, Thursday, October 28, 2021

**Venue**: Clements Hall 126

**Title**: Direct solvers for elliptic PDEs

**Speaker**: Gunnar Martinsson, Oden Institute, UT Austin

**Abstract**: That the linear systems arising upon the discretization of elliptic PDEs can be solved efficiently is well-known, and iterative solvers that often attain linear complexity (multigrid, Krylov methods, etc) have proven very successful. Interestingly, it has recently been demonstrated that it is often possible to directly compute an approximate inverse to the coefficient matrix in linear (or close to linear) time. The talk will describe some recent work in the field and will argue that direct solvers have several advantages, including improved stability and robustness, the ability to solve certain problems that have remained intractable to iterative methods, and dramatic improvements in speed in certain environments.

**Biography: **Gunnar Martinsson is a Professor of Mathematics at the University of Texas at Austin, where he also holds the W.A. “Tex” Moncrief, Jr. Chair in Simulation-Based Engineering and Sciences in the Oden Institute for Computational Engineering and Sciences. Prior to joining UT Austin, Martinsson served as a Professor of Mathematics at the University of Oxford, and he has previously held faculty positions at the University of Colorado at Boulder and at Yale University. He earned his Ph.D. in computational and applied mathematics in 2002 from UT Austin. He received a M.Sc. degree in Engineering Physics in 1996 and a “Licentiate” degree in Mathematics in 1998, both from the Chalmers University of Technology in Sweden. Martinsson was the recipient of the SIAM 2017 Germund Dahlquist Prize, and was named a Fellow of SIAM in 2021.

Martinsson’s research concerns the development of faster algorithms for ubiquitous computational tasks in scientific computing and data sciences. Recent work has focused on randomized methods in linear algebra, fast solvers for elliptic PDEs, O(N) complexity direct solvers, structured matrix computations, and high order accurate methods for scattering and fluid problems